The three-dimensional reference interaction site model with the closure relation by Kovalenko and Hirata (3D-RISM-KH) provides the solvent structure in the form of a 3D site distribution function, \(g_{\gamma}^{UV}(r)\), for each solvent site, \(\gamma\). Note that the use of 3D-RISM as implemented in ADF is an expert option.

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It enables, at modest computational cost, the calculations of thermodynamics, electronic properties and molecular solvation structure of a solute molecule in a given molecular liquid or mixture. Using 3D-RISM, one can study chemical reactions, including reaction coordinates and transition state search, with the molecular solvation described from the first principles. The method yields all of the features available by using other solvation approaches. The 3D-RISM part of ADF has not been parallelized.

Details on the implementation of 3D-RISM-KH in ADF can be found in Ref. [300], with applications in Ref. [301]. The theory of 3D-RISM-KH in combination with DFT can be found in Refs. [302-304, 349]. A combination of 3D-RISM-KH with FDE (frozen-density embedding) can be found in Ref. [305].

Similar to explicit solvent simulations, 3D-RISM properly accounts for chemical peculiarities of both solute and solvent molecules, such as hydrogen bonding and hydrophobic forces, by yielding the 3D site density distributions of the solvent. Moreover, it readily provides, via analytical expressions, all of the solvation thermodynamics, including the solvation free energy potential, its energetic and entropic decomposition, and partial molar volume and compressibility. The expression for the solvation free energy (and its derivatives) in terms of integrals of the correlation functions follows from a particular approximation for the so-called closure relation used to complete the integral equation for the direct and total correlation functions.

If one assumes that the internal energy and the vibrational and rotational entropy of the solute molecule is the same in solution and in gas phase, then this simplifies to:

Solvation Free Energy =

[ (Total Bonding Energy) + (Excess Chemical Potential) ]_3D-RISM

- [ (Total Bonding Energy)]_Gas-Phase

However, a formally accurate calculation should include the difference between the thermal corrections from frequency calculations produced by ADF in the SCF calculation with 3D-RISM-KH solvation and in gas phase.

Input

When performing 3D-RISM simulations, each atom in the ATOMS block must have two parameters specified, SigU and EpsU, for example:

ATOMSC0.000.000.00SigU=3.50EpsU=0.066...END

The SigU and EpsU parameters have the same meaning as Sigma_alpha and Eps_alpha for atoms of the solvent in the SOLVENT sub-block below. They can be obtained from a Lennard-Jones force-field parameter sets.

All 3D-RISM-related input keys are contained in a RISM input block. Below, only the mandatory keywords are shown. Optional keywords are described in the next section.

The RISM1D sub-block contains general parameters for the 1D-RISM calculation of the solvent(s). Even though all RISM1D sub-keys have reasonable defaults, the FLUIDPARAM sub-key deserves a special attention because its default values are only applicable if the solvent is water. Thus, you may need to change some of these values when modeling a different solvent, at least the dielectric constant and the density. Note that even when using all default values from the RISM1D sub-block the sub-block itself must be specified, even if empty. See below for complete description of the RISM1D sub-block.

The SOLVENT sub-block can be repeated if the solvent is a mixture. Each SOLVENT sub-block contains parameters for one solvent. First, each solvent has a name, which is specified on the SOLVENT keyword’s line and is arbitrary. The first line in the SOLVENT sub-block must contain the UNITS key. You should leave it at the default values. Then follow the actual solvent parameters. In principle, each solvent consists of multiple atoms and functional groups. For simplicity, we will call each of them an atom. For example, in 3D-RISM therms, methanol consists of 3 “atoms”: CH3 , O, and H. Each such atom has a set of three parameters, shared between all atoms of the same type, and the coordinates. These parameters follow the PARAMETERS keyword. The line with the PARAMETERS keyword itself must specify the molecular weight of the solvent and the number of atom types that follow. The first line for each atom type contains, in this order: number of atoms of this type, \(z_\alpha\) , \(\sigma_\alpha\) , \(\epsilon_\alpha\) , three coordinates for the first atom of this type. If there is more than one atom of this type then the coordinates for the 2nd and other atoms follow on subsequent lines. The SOLVENT sub-block is concluded by the specific density of this solvent, by default, in molecules per cubic angstrom. This number should be equal to the total density for mono-component solvents.

The SOLUTE sub-block specifies 3D-RISM parameters for your molecule. The BOXSIZE and BOXGRID sub-keys specify dimensions of the simulation box, in Angstrom, and the number of points of grid in each direction. The box should be twice as large as the molecule and the BOXGRID values must be a power of 2. The size/np ratio defines the grid spacing in each direction and this should be not larger than 0.5 angstrom.

The optional 3D-RISM keys for the RISM1D and SOLUTE sub-blocks are listed below together with their defaults.

Xvvfile - name of the file with the results of the 1D-RISM calculation specified in the RISM1D keyword above, with .xvv appended to it;

Outfile - name of the output text file;

Output - print level;

CHRGLVL - which charges computed by ADF to use. This can be MDCq (default), MDCd, MDCm, or EXACT. The Nis, DELOZ, and TOLOZ have the same meaning for 3D-RISM as parameters of the MDIIS keyword of the RISM1D block. Likewise, Ksave, Kshow, and Maxste are analogous to the parameters of the ITER key in RISM1D.